In recent years, stereoscopic luminous characters become the first choice for billboards because of their attractive and high-grade appearances and low cost. The edge of a stereoscopic luminous character is usually made to form a grooved character with an aluminum alloy sheet and a stainless steel sheet, and the intermediate part is filled by an LED luminous board or a common plastic sheet. The main work of making a stereoscopic luminous character edge is edge enclosure which mainly includes edge bending and arc curving. Traditional edge bending and arc curving are manual processes or using a cutting blade to carry out grooving followed by machining, thereby costing time and labor and having ugly appearance. Using a stainless steel sheet to make a grooved character requires high-pressure water jet to make a hollow-out character, and the high-pressure water jet has the power usually over 10 KW and is not so fast in cutting speed, therefore its cost is high and energy consumption is large. After the hollow-out character is made by cutting, an edge band needs to be welded to form a character shell. Edge band welding costs time and labor and has heat emission. Some advertisement companies use very thick stainless steel for making a hollow-out character to show their high-grade produces, and it costs long cutting time and high energy consumption. In order to provide a special device, the applicant has disclosed a stereoscopic luminous character enclosing machine (patent No.: 200710113527.5), which includes a feeding unit mounted on a main board of a machine body, a groove-cutting unit and an arc-curving unit, wherein the groove-cutting unit includes a traversing rack and an elevating rack mounted on the traversing rack, the traversing hack and the elevating rack are respectively driven by a motor through a ball screw, a motor-driven saw disc is mounted on the elevating rack, an arc-curving pressure roller elevating unit is mounted on the traversing rack, and an arc-curving pressure roller capable of passing through the main board of the machine body is disposed on the upper end of the arc-curving pressure roller elevating unit. This luminous character enclosing machine has the disadvantages as follows: first, heat is easily generated during cutting due to use of the saw disc for grooving, resulting in discoloration of a stainless steel band, and thus the machine is not suitable for groove-cutting of a stainless steel band; second, when a luminous character edge is completed, manual breaking is needed, which is unfavorable for automatic operation of the whole machine.